The chirp modulation method is a modulation method in which the frequency of a signal (chirp) varies linearly over time in a bandwidth of Fs Hz. A chirp having a positive gradient in the frequency-time plane is generally referred to as an up-chirp, for example chirp 1 and chirp 2 on FIG. 1. A chirp having a negative gradient in the frequency-time plane is generally referred to as a down-chirp, for example chirp 3 on FIG. 1.
A chirp can be represented by a sequence of N samples. One or more identical contiguous chirps can form a symbol that represents a data value to be communicated. A chirp can be represented mathematically as:C(g,p)=ejπg(n−fn(p))(n+1−fn(p))/N   (equation 1)where g is the gradient of the chirp, N is the number of samples in the sequence, n is a sample in the sequence, p is the symbol's value, fn(p) is a function that encodes p onto the received chirp, which implicitly may also be a function of g, n, N and other constants, and C is the received chirp sequence, which is normally evaluated for all integer values of n from 0 to N−1 in order. The number of valid values of p is the symbol set size, which is nominally N. However, the symbol set size can be more or less than N depending on the quality of the link. The value of g can have any value greater than 0 and less than N. Preferably, g is an integer between 1 and N−1. Due to the modular nature of this expression negative gradients are obtained from N−1 backwards. Hence, N−2 is equivalent to a negative gradient of −2. Where there are more than one identical contiguous chirps in a symbol, each chirp individually conveys the same value which is the symbol value of the symbol.
Chirp 1 in FIG. 1 has a starting frequency of −Fs/2 and a gradient of 1. It increases linearly in frequency over a period of N samples at a sample rate of Fs to reach a frequency close to +Fs/2. Since this is a complex sampled system +Fs/2 is the same as −Fs/2. Multiple chirps are usually contiguous but may start with a different frequency. The signal phase is typically made continuous throughout a sequence of chirps. In other words, after the signal has reached +Fs/2 at n=N−1, the next symbol starts with n=0 again. FIG. 1 illustrates an example in which two consecutive chirps have the same symbol value, whereas the third chirp is different. An apparent discontinuity in frequency between chirp 1 and chirp 2 occurs at n=N.
Chirp 4 in FIG. 2 has a gradient of 2 and a starting frequency of −Fs/2. Because it has double the gradient of the chirps of FIG. 1, it increases linearly in frequency to +Fs/2 in half the number of samples that the chirps in FIG. 1 do, i.e. it reaches close to +Fs/2 after close to N/2 samples. The chirp then wraps around in frequency. Since this is a sampled system, these frequency wraps are in effect continuous and have continuous phase. The chirp repeats the frequency sweep from −Fs/2 to +Fs/2 between samples N/2 and N.
The chirps also have continuous frequency and phase from one end of the chirp to the other. A cyclic shift of the samples that make up a chirp creates another valid chirp.
Chirp communications are typically used in systems operating using low data rates and short messages. In such systems, the transmitter typically transmits messages periodically, for example a remote temperature tag may periodically transmit a message indicating a measured temperature. Typically, the transmitter does not know the location of the receiver or receivers which are to receive the message it transmits. Reliable receipt of the transmission at distal receivers as well as close by receivers is desirable. One solution is to transmit the messages with sufficiently high power to be detectable by all receivers within a predetermined range. However, chirps signals are typically communicated between low power devices, for example battery powered handheld devices and in environments where there could be multiple simultaneous transmitting devices. Transmission of frequent high power signals causes an undesirable drain on the power reserves of a battery powered device, and also causes undesirable interference to other users of the system.
Rather than transmitting at a high power, another solution to enable reliable receipt of the transmission at a distal receiver is to increase the sensitivity of the receiver by adding error correction bits, for example forward error correction (FEC). However, FEC requires the transmission of additional bits, which incurs additional delay and requires more energy. FEC is suitable for higher value communications systems where large numbers of silicon gates are acceptable. Chirp communications allow for low power and small silicon area solutions and are targeted at very high volume and very lost cost markets. Hence, additional gates for FEC circuitry, in both the transmitter and receiver, are proportionally expensive and power hungry.
Thus, there is a need for an improved method of communicating a chirp signal from a transmitter to a receiver that increases the receiver sensitivity, but that is suitable for a communication system operating using small silicon areas, low power and short messages and in environments where there could be multiple simultaneous transmitting devices.